Method for determining effective coefficient of thermal expansion

ABSTRACT

A method for determining an “effective” thermal coefficient of a machine comprises the steps of installing one or more temperature sensors ( 110 ) at various locations on the machine, positioning a first machine member ( 60 ) at a “known” reference Location, relative to a second machine member ( 42 ), installing a linear position measuring device ( 120 ) to detect changes in position of the first machine member ( 60 ) relative to the second machine member ( 42 ) along a first axis of movement, periodically acquiring readings from each of the temperature sensors ( 110 ) and from the linear position measuring device ( 120 ) during a test cycle and compiling the temperature and linear position data into a table. A statistical correlation analysis is performed to determine which of the temperature sensors ( 110 ) experiences changes in temperature are most linearly related to changes in the linear position of the first machine member ( 60 ) relative to the second machine member ( 42 ) and an “effective” coefficient of thermal expansion is thereafter determined as the rate of change of position, i.e. length, relative to change in temperature. The present method includes using the machine&#39;s “effective” thermal coefficient to calibrate the motion of the machine to compensate for the thermal characteristics thereof.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to methods for determining linearpositioning inaccuracies of a moving member of a machine due to thermalexpansion of the machine member and of the machine. More particularly,the present invention relates to a method for determining linearpositioning inaccuracies of a moving member of a machine due to thermalexpansion of the machine member and of the machine, wherein an effectivecoefficient of thermal expansion of the machine is derived empirically,and wherein such effective coefficient of thermal expansion is used tocompensate for such positioning inaccuracies.

[0002] Large metal-working machines, such as, for example, gantry-stylemachine tools (oftentimes referred-to by those skilled in the art as“profiler machines”), are constructed largely out of structural steel.Like other materials used to construct machine members, steel possessesa metallurgical property which causes a machine member constructedtherefrom to deform linearly in response to changes in its temperature.For example, a machine member of a long-travel machine tool—such as anelongate rail upon which another machine member rides—constructed out ofsteel and having a fixed length L, will change linearly in length due tochanges in the temperature thereof an amount equal to:

ΔL=L·αΔT  (1)

[0003] where:

[0004] ΔL=a change in length of the member,

[0005] L=an initial length of the member at an initial temperature T_(i)thereof;

[0006] α=the coefficient of thermal expansion (“thermal coefficient”);and,

[0007] ΔT=a change in temperature of the member=T_(f)−T_(i), where:

[0008] T_(f)=a temperature of the member.

[0009] The thermal coefficient α is the rate at which a change in thelength of the machine member ΔL will be directly proportional to achange in the temperature ΔT thereof and is a property of the specificmaterial used to construct the member. Accordingly, the thermalcoefficient α is used to calculate both increases in the length of amachine member due to increases in the temperature thereof, as well asdecreases in the length of the machine member due to decreases in thetemperature thereof. However, for the purpose of clarity andillustration, the within description will refer only to increases in thelength of the machine member due to increases in the temperaturethereof, although such description shall apply equally to decreases inthe length of the machine member due to decreases in the temperaturethereof without departing from either the spirit or the scope of thepresent invention.

[0010] The value of the thermal coefficient α for most materials isconsidered by those skilled in the art to be constant through a widerange of temperatures, including standard “room” temperature of 68° F.(20° C.), which is accepted by those skilled in the art as being asuitable (albeit generalized) baseline temperature for most thermalexpansion calculations. As such, thermal expansion measurements andcalculations typically are performed with reference to the initialtemperature T_(i) of the machine member being 68° F. (20° C.). Forconvenience, “textbook” values of common thermal coefficients a whichare based on an initial temperature of 68° F. (20° C.) are usedtypically in performing these calculations.

[0011] However, the “true” value of the thermal coefficient may bedifferent from the “textbook” value thereof and thermal expansionmeasurements and calculations of machine members based on a “textbook”value of the thermal coefficient α may lead to inaccurate calculations,albeit generally of small magnitudes. Nevertheless, in machiningoperations, such as those typically performed by profiler machines,where high degrees of machining accuracy are required, even minimallyinaccurate calculations may lead to significant dimensional machiningerrors. It is therefore desirable to provide a method for determiningthe “effective” value of the thermal coefficient α of a machine member.It is also desirable to provide a method for determining the “effective”value of the thermal coefficient α of a machine member, with referenceto the environmental conditions surrounding it.

[0012] Machines typically are not comprised only of a single element,but rather, include combinations of numerous elements, parts, componentsor members which are fixedly, slidably, rotatably or otherwiseoperatively connected to one another to form an interrelated, operativestructure. For example, a profiler machine typically comprises threemain sub-structures: 1) a bed upon which a workpiece is secured; 2) ahead supported over the bed for positioning a cutting tool in closeproximity to the workpiece for performing machining operations thereon;and, 3) a rail system for supporting the head over the bed and forproviding movement of the head with respect to the bed along an elongateaxis thereof. Each of the three main sub-structures includes numerousparts operatively engaging one another for performing machiningoperations according to a preselected design configuration, and eachsuch part has thermal properties according to the material from whichsuch part is constructed. As the temperature of each member increases,for example, due to an increase in the temperature of the airsurrounding the machine (thereby increasing the temperature of the partitself) the members individually experience thermal expansion at a rateequal to the thermal coefficient α of the material from which the memberare respectively constructed It would not be uncommon for the parts tobe constructed from different materials, in which case each materialtypically will have a unique thermal coefficient α, and the parts of themachine will expand at different rates leading to non-uniform expansionof the machine. It is desirable therefore to provide a method fordetermining an “effective” value of the thermal coefficient α of amachine comprised of members constructed of materials having differingindividual thermal coefficients a.

[0013] Moreover, in a conventional machine, the members thereof areconstrained from moving freely because the members are operativelyconnected to other machine members, as well as to support structures.For example, the rail system of a conventional profiler machinecomprises a pair of elongate rails along which the head traverses. Therails are fixedly anchored to the machine shop floor by severalstructural bolts, thereby limiting the free thermal elongation of therails. Because machining accuracy depends directly on the accuratepositioning of the head along the rails, it is necessary to be able tocalculate how the rails expand in response to increases in thetemperature thereof. However, because the rails are constrained,conventional thermal expansion calculations based upon “textbook” valuesof the thermal coefficient α likely will not accurately predict theexpansion of the rails due to increases in the temperature thereof.Accordingly, it is desirable furthermore to provide a method fordetermining the “effective” value of the thermal coefficient α of amachine comprised of members which are constrained from freely moving inresponse to changes in the temperatures thereof.

[0014] The size and geometry of conventional machine tools, such asprofiler machines, oftentimes results in localized heat pockets beingcreated at isolated locations of the machine members, thereby givingrise to localized rates of thermal expansion which are different fromthe rates of thermal expansion at other locations of the machine and ofthe machine members. That is, the temperature of the machine varies(sometimes widely) across the entire machine, making it difficult todetermine where to measure the temperature of the machine, for example,for the purpose of performing “textbook” thermal expansion calculations.Accordingly, it is desirable furthermore to provide a method fordetermining an “effective” temperature of the machine, which such“effective temperature” thereof may be used, for example, in performingthermal expansion calculations.

[0015] It is known that machine tools must be calibrated fromtime-to-time to correct for mechanical and thermal positioning errors.However, while conventional machine calibration practices may adequatelycompensate for mechanical positioning errors, they incorporate only“textbook” values of thermal coefficients, and as such, machinecompensation tables resulting therefrom do not adequately consider theunique thermal characteristics of the machine being calibrated.Accordingly, it is desirable furthermore to provide a method forcalibrating a machine wherein the true thermal characteristics of themachine are closely approximated, such as, with reference to an“effective” thermal coefficient thereof. Moreover, conventional machinecalibration practices do not consider the thermal characteristics of aworkpiece being machined thereby. That is, machine compensation tablesresulting from conventional machine calibration practices are notadapted to be modified for machining workpieces constructed out ofmaterials having thermal characteristics differing significantly fromthe thermal characteristics of the machine. For example, an aluminumworkpiece will expand at a rate much greater than the rate at which aprofiler machine will expand and the machine compensation tablesresulting from conventional machine calibration practices reflect onlythe thermal characteristics of the machine, which will result inmachining inaccuracies unless the NC “part program” used to instruct themachine for performing machining operations is modified to account forthe unique thermal characteristics of the workpiece relative to thethermal characteristics of the machine. Oftentimes, such modificationmust be performed manually by an NC programmer or are incorporated intoso-called “post-process” modification of the NC program It is desirabletherefore to provide a method for calibrating a machine wherein thethermal characteristics of a workpiece to be machined thereby areincorporated thereinto. It is desirable even further to provide a methodfor calibrating a machine wherein the thermal characteristics of aworkpiece to be machined thereby are incorporated thereinto, and whereina plurality of workpiece materials may be considered.

SUMMARY OF THE INVENTION

[0016] The present invention is for a method for determining an“effective” thermal coefficient of a machine comprised of members andfor a method for using such effective thermal coefficient to calibratethe machine and of the members thereof for thermal expansion thereof.The method for determining an “effective” thermal coefficient of amachine according to the preferred embodiment hereof comprises the stepsof installing one or more temperature sensors, such as conventionalthermocouples, at various locations on the machine, positioning a firstmachine member at a known “reference” location, relative to a secondmachine member, installing a linear position measuring device to detectchanges in position of the first machine member relative to the secondmachine member along a first axis of movement, periodically acquiringreadings from each of the temperature sensors and from the linearposition measuring device during a test cycle and compiling thetemperature and linear position data into a table. The test cyclepreferably is a period of time, for example, 24 hours to 48 hours,during which diurnal temperature variation of the environmentsurrounding the machine will occur. A statistical correlation analysis,such as by using the Pearson Product Moment Correlation Coefficient, isperformed to determine which of the temperature sensors experienceschanges in temperature which are most linearly related to changes in thelinear position of the first machine member relative to the secondmachine member. An “effective” coefficient of thermal expansion isthereafter determined as the rate of change of position (or length)relative to change in temperature. The position of the temperaturesensor which most linearly relates to changes in the linear position ofthe first machine member relative to the second machine member, then,defines the location of the “effective” temperature of the machine.

[0017] The present invention also relates to a method of using themachine's “effective” thermal coefficient to calibrate the motion of themachine to compensate for the thermal characteristics thereof. That is,compensation tables resulting from the machine calibration procedure arebased at least partly on the “effective” thermal coefficient of themachine. The compensation table may be modified to take into account thethermal characteristics of a workpiece to be machined, which suchworkpiece may be constructed from any one of a plural of materialshaving differing thermal coefficients. Compensation table can be changedaltogether to permit machine compensation for different workpiecematerials. Compensation table selection can be manual, such as by anoperator selecting an option on the machine control, or automatic, suchas by a program instruction in the part program.

[0018] According to one aspect of the present invention, the presentinvention provides a method for calibrating a machine to compensate forthermal expansion/contraction thereof characterized in that the methodcomprises the steps of determining an effective thermal coefficient ofthe machine, and generating a machine thermal compensation value for atleast one of a predetermined number of preselected position values, themachine thermal compensation value being based on the effective thermalcoefficient of the machine.

[0019] It is an object of the present invention to provide a method fordetermining an “effective” value of the thermal coefficient of a machinemember or machine.

[0020] It is another object of the present invention to provide a methodfor determining an “effective” value of the thermal coefficient of amachine member or machine, with reference to the environmentalconditions surrounding it.

[0021] It is still another object of the present invention to provide amethod for determining an “effective” value of the thermal coefficientof a machine comprised of members constructed of materials havingdiffering individual thermal coefficients.

[0022] It is yet another object of the present invention to provide amethod for determining an “effective” value of the thermal coefficientof a machine comprised of members which are constrained from freelymoving in response to changes in the temperatures thereof.

[0023] It is still another object of the present invention to provide amethod for determining an “effective” temperature of a machine member ormachine, which such “effective temperature” thereof may be used, forexample, in performing thermal expansion calculations.

[0024] It is another object of the present invention to provide a methodfor calibrating a machine wherein the true thermal characteristics ofthe machine are closely approximated, such as, with reference to an“effective” value of a thermal coefficient thereof.

[0025] It is still another object of the present invention to provide amethod of calibrating a machine wherein the thermal characteristics of aworkpiece to be machined thereby are incorporated thereinto.

[0026] It is another object of the present invention to provide a methodfor calibrating a machine where the thermal characteristics of aworkpiece to be machined thereby are incorporated thereinto, and whereina plurality of workpiece materials may be considered.

[0027] These and additional objects, features and advantages of thepresent invention will become apparent to those reasonably skilled inthe art from the description which follows, and may be realized by meansof the instrumentalities and combinations particularly pointed outtherein

BRIEF DESCRIPTION OF THE DRAWINGS

[0028] A better understanding of the present invention will be had uponreference to the following description in conjunction with theaccompanying drawings in which like numerals refer to like parts, andwherein:

[0029]FIG. 1 is a schematic perspective view of a conventionalgantry-style machine tool;

[0030]FIG. 2 is a schematic perspective view of the machine tool of FIG.1, showing instrumentation installed thereon for use with the methodaccording to a preferred embodiment of the present invention;

[0031]FIG. 3 is a plot of machine “drift” versus temperature used todetermine an “effective” coefficient of the thermal expansion of themachine tool of FIG. 1 according to a preferred embodiment of thepresent invention;

[0032]FIG. 4 is a schematic representation of a compensation table usedto compensate for thermal expansion of the machine of FIG. 1 accordingto a preferred embodiment of the present invention; and,

[0033]FIG. 5 is a schematic representation of a compensation table usedto compensate for thermal expansion of the machine of FIG. 1, as well asfor thermal expansion of the workpiece of FIG. 1, according to apreferred embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0034] with reference to FIG. 1, a gantry-style machine tool 10(sometimes referred-to herein as a “profiler” machine) includes anelongate bed 20 resting on pads 22 and being anchored to the machineshop floor, such as, by structural bolts (not shown), connecting the bed20 to the floor through the pads 22. A lengthwise direction of the bed20 defines an “X” axis thereof. The bed 20 preferably is constructedfrom a single piece of structural steel (as shown) having asubstantially continuous planar work surface 24 which is machined tohave a flat, uniform finish. Alternatively, the bed 20 may beconstructed from a plurality of sections (not shown), in which case thesections are connected to one another to form the work surface 24.

[0035] A workpiece-holding device 26 is securely affixable to the worksurface 24 at any number of a plurality of locations thereon and isadapted to securely hold a workpiece “W” thereto. Alternatively, theworkpiece “W” may be securely affixed to the work surface 24, such as,by clamping, in which case, the workpiece-holding device 26 is notnecessary.

[0036] First and second elongate rails 40, 42, respectively, resting onpads 44, are positioned alongside the bed 20, spaced transverselytherefrom along a transverse direction along axis “Z”, which isperpendicular to axis “X”. The rails 40, 42 extend in a directionparallel to the “X” axis, and are mounted to the machine shop floor,such as, by structural bolts (not shown) such that the rails 40, 42 areparallel to one another. The rails 40, 42 preferably are constructedfrom structural steel and include upper bearing surfaces 41, 43 whichhave been machined to have a flat, uniform finish. The rails 40, 42 maybe separate from the bed 20 (as shown) or may form an integralconstruction with the bed 20. The bearing surfaces 41, 43 may bemachined directly on the rails 40, 42, respectively, or alternatively,may be in the form of elongate rail caps (not shown) which are affixedto the rails 40, 42.

[0037] A machining head 60 is supported over the bed 20 by rails 40, 42and is movable relative thereto along the “X” axis of the bed 20. Forexample, the head 60 includes first and second upright supports 62, 64having upper ends thereof connected to one another by an overhead bridgestructure 66. A lower end of the first upright support 62 is sidablypositioned along the first rail 40 and a lower end of the second uprightsupport is slidably positioned along the second rail 42 such thatsimultaneous movement of the supports 62, 64 along the rails 40, 42positions the overhead bridge 66 at any of an infinite number oflocations along the “Y” axis of the bed 20.

[0038] The machining head 60 is movable along the rails 40, 42, such as,by a rack-and-pinion assembly 80, shown schematically in FIG. 1 anddescribed herein with reference to the second rail 42. Therack-and-pinion assembly 80 includes an elongate rack 82 mounted to therail 42, extending therealong parallel to axis “X”. A reversible motor84 or other similar drive device is mounted to the second uprightsupport 64, such as, by bracket 85, such that a pinion 86 mounted to anoutput shaft (not shown) of the motor 84 positively engages the rack 84.A similar rack-and-pinion assembly 80 is provided on the first rail 40.Rotation of the pinion 86, then, such as, by energizing the motor 84,drives the machining head 60 along the rails 40, 42. Alternatively, therack-and-pinion assembly 80 may be replaced with another linear drivedevice, such as a conventional ballscrew drive assembly or aconventional linear servomotor drive assembly.

[0039] The machining head 60 also includes a transverse carrier 70slidably mounted to the overhead bridge 66 for movement of thetransverse carrier 70 along horizontal ways 71 in a direction parallelto the “Z” axis. The transverse carrier 70 may be driven by anyconventional linear drive device (not shown), such as a rack-and-pinionassembly, a ballscrew drive assembly, a linear servomotor assembly orthe like. A spindle carrier 74 is slidably mounted to the transversecarrier 70 for movement of the spindle carrier 74 along vertical ways 75in a direction parallel to the “Y” axis. The spindle carrier 74 may bedriven by any conventional linear drive device (not shown), such as arack-and-pinion assembly, a ballscrew drive assembly, a linearservomotor assembly or the like.

[0040] A spindle 90 is mounted to a lower end of the spindle carrier 74,such as, by bracket 92 such that the spindle 90 is adapted to pivotabout a “C” axis, which is parallel to the “X” axis. The spindle 90 isadapted to hold, such as, for example, by a chucking device (not shown),a conventional cutting tool 93. Movement of the cutting tool 93,relative to the workpiece “W”, then, may be along any combination offour axes; namely, the “X” axis, the “Y” axis, the “Z” axis and the “C”axis. Additional degrees of movement of the cutting tool 93, relative tothe workpiece “W”, may be added according to structures and techniquesknown to those skilled in the art. Moreover, spindle 90 may be mountedto carrier 74 without provision for movement about the “C” axis, inwhich case, spindle 90 would direct tool 93 in a direction, for example,parallel to axis “Y”, axis “Z”, or any oblique axis relative thereto.The configuration of the machine tool 10 described herein is for thepurpose of illustration only and the present invention is not limitedthereto, but rather, may be practiced on any machine, subassembly orcomponent thereof, which may become obvious to one of ordinary skill inthe art upon reading the within description.

[0041] With reference to FIG. 2, the machine tool 10 is prepared fordetermining an “effective” coefficient of thermal expansion a (“thermalcoefficient”) of the machine tool 10 according to a preferred embodimentof the present invention. Although the method according to the preferredembodiment hereof will be described with reference to expansion of thesecond rail 42 of the machine tool 10 along the “X₂” axis, it will beobvious to those of ordinary skill in the art, upon reading the withindetailed description, that the method according to the preferredembodiment hereof may be modified to determine the coefficient ofthermal expansion a of the machine tool 10 (or of any member thereof)along any axis without departing from either the spirit or the scopehereof For example, the method of the present invention may be used todetermine an “effective” coefficient of thermal expansion to calibratemovement of the transverse carrier 70 along horizontal ways 71 in the“Z” direction or to calibrate movement of the spindle carrier 74 alongways 75 in the “Y” direction.

[0042] In the exemplary embodiment hereof the “effective” thermalcoefficient α will be derived empirically for the purpose of calibratingmovement of the head 60 along the rails 41, 42 and will be describedwith reference to second rail 42. As stated above, owing to thermalexpansion characteristics of the material used to construct the rail 42,the length of the rail 42 will be different at 68° F. (20° C.) roomtemperature than under normal operating circumstances, where thetemperature is usually greater than 68° F. (20° C.) room temperature.The difference between the length L of the rail 42 at 68° F. (20° C.)room temperature and the length L of the rail 42 at normal operatingconditions is quantified and represented herein as ΔL, the change in thelength thereof owing to thermal expansion of the rail 42. Changes in thelength of the rail 42 are desired so that the machining head 60 can bepositioned along the “X” axis accurately, relative to the workpiece “W”,while taking into account thermal expansion of the rail 42 along the “X”axis.

[0043] One or more temperature sensors 110, such as, for example,conventional thermocouples, are installed at various locations acrossthe bed 20, the rails 40, 42 and the machining head 60. The quantity andpositioning of the sensors 110 is determined based upon known operatingconditions of the machine 10. That is, an operator who is skilled withoperation of the machine 10 may know from fist-hand experience thatcertain locations on the machine 10 experience local “hot spots,” inwhich case, the operator may choose to install several sensors 110 inthe general region of such a “hot spot” Similarly, the operator may knowfrom first-hand experience that certain locations on the machine 10experience substantially uniform temperature distribution, in whichcase, the operator may choose to install only one sensor 110 in thislocation. For example, several criteria may be used to determine thequantity and positioning of the sensors 110, such as, the axis of themachine being tested, the feedback system of the machine, factory airtemperature control vents, heat sources of the machine and the machineenvironment, generally.

[0044] In the exemplary embodiment, nine sensors 110 are used, three ofwhich are installed equally-spaced along the first rail 40 (only two ofwhich are shown), three of which are installed equally-spaced along thesecond rail 42 (only two of which are shown) and three of which areinstalled equally-spaced along the “X” axis of the bed 20. The sensors110 may be installed on the surface of the machine 10, or may beembedded therein, such as by drilling a hole in the machine 10 andinserting the sensor 110 in the hole formed thereby. The sensors 110 areelectronically coupled, such as by cables (not shown), to a datacollection device 115, such as a laptop personal computer (“PC”) havingsufficient conventional hardware and software for interfacing with thesensors 110 and for reading and recording temperatures detected thereby.

[0045] A linear position measurement device 120, such as a model HP5529Alaser measuring device sold by Agilent Technologies of Palo Alto,Calif., is installed at a front end of the rail 42 and aligned with asecond rail axis “X₂”, which such second rail axis “X₂” is parallel tothe “X” axis of the bed 20, to measure the position of the head 60relative to the rail 42 therealong. The laser measurement device 120includes a laser transmitter/receiver 121 positioned in front of therail 42 and aligned with the second rail axis “X₂” to transmit a laserlight beam along the second rail axis “X₂” towards the head 60, aninterferometer 122 mounted near the front of the rail 42 and a linearretroreflector 123 mounted to the second upright support 64 of the head60. The interferometer 122 and the retroreflector 123 are aligned withthe transmitter/receiver 121 along the second rail axis “X₂”. Thetransmitter/receiver 121 is electronically coupled to the PC 115, whichis adapted to receive data from the transmitter/receiver 121 and tostore the data, along with temperature data acquired from the sensors110. The laser measuring device 120 is calibrated to accurately measure,using conventional techniques, a distance “D” between the interferometer122 and the retroreflector 123, which of course, is a function of bothtime and temperature. The linear measurement device 120 is calibratedaccording to the manufacturer's instructions, and where auxiliarysensors have been provided with the device 120 to obtain environmentalconditions data, for example, air temperature, pressure and humidity—allof which may affect the accuracy of the linear measurement device120—such sensors are installed and enabled such that the device 120 isprepared to obtain highly accurate measurements. If the control systemof the device 120 requires a value of the thermal coefficient α of themachine 10, a value of zero should be entered such that no analyticalcorrection of the linear measurements obtained by the device 120 owingto thermal expansion thereof is made, but rather, such that the device120 obtains (and records) the true value of any linear measurementsdetected thereby. It will be readily understood by those skilled in theart that the laser measurement device of the exemplary embodiment, andthe components thereof, are described herein for the purpose ofillustration only and the present invention is not limited to this typeof linear measurement device, but rather, any device which is suitablefor accurately measuring small changes in distance, for example, on theorder of ±0.00001 inches (0.25 microns), may be substituted for thelaser measurement device without departing from either the spirit or thescope hereof.

[0046] The PC 115 includes software which is adapted to receivemeasurements from the sensors 110 and from the linear positionmeasurement device 120 and to tabulate the data acquired thereby. Thesoftware is adapted to periodically acquire data from the sensors 110and from the linear position measurement device 120, for example, every10 minutes, for a predetermined extended period of time, for example, 24hours, which such extended period of time has been selected to accountfor diurnal variations in the temperature of the machine 10. Of course,temperature and position measurements may be obtained at anypredetermined interval (for example, more or less than 10 minutes) andfor any predetermined test period (for example, more or less than 24hours).

[0047] The method of determining the “effective” thermal coefficient αaccording to the preferred embodiment hereof will now be described.After the machine tool 10 has been prepared as described above and shownin FIG. 2, the head 60 is moved to the near end (adjacent theinterferometer 123) of the rails 40, 42 and the linear measurementdevice 120 is “zeroed”, thereby defining a “home” position of the head60, relative to the rails 42. The head 60 is then moved to the far endof the rails 40, 42 (as shown) and “parked” in this position. Thedistance traveled by the head 60 from the “home” position to the“parked” position, as measured by the measurement device 120, isrecorded by the PC 115 and is identified as the test length “L_(T)”. Themeasurement device 120 is again “zeroed”, thereby defining a “referencetest position”.

[0048] The test procedure software, which has been installed on the PC115 is initiated and will run for the predetermined test period, whichin the preferred embodiment hereof is 24 hours. At some predeterminedfrequency, which in the preferred embodiment hereof has a period of 10minutes, the test procedure software acquires a temperature reading fromeach of the sensors 110 and a position reading from the linearmeasurement device 120 and stores these readings in a table in thememory (or some other suitable storage media) of the PC 115. Theposition reading acquired from the linear measurement device 120 at theend of the 10-minute interval corresponds to the position of the head 60relative to the “reference test position” and is a measure of theso-called “drift” of the head 60 from the “reference test position” dueto thermal expansion/contraction of the machine 10, or moreparticularly, due to thermal expansion/contraction of the rail 42. Head“drift” from the “reference test position”, then, will be known for each10-minute interval of the test procedure. Using the nomenclature statedabove with respect to thermal expansion calculations, the thermal“drift” is represented by the change in length ΔL of the rail 42 due tothermal expansion/contraction.

[0049] Once the test procedure is complete, a statistical correlationanalysis is performed on the data acquired by the temperature sensors110 and the linear measurement device 120 and stored in the memory (oron some other suitable storage media) of the PC 115 to determine whichof the sensors 110 detects a temperature change ΔT which most directlycorrelates to a linear change in the length ΔL of the rail 42. Althoughany suitable statistical model may be used, a Pearson Product MomentCorrelation Coefficient preferably is calculated for each temperaturesensor 110, using the data acquired thereby, according to the followingequation: $\begin{matrix}{R = \frac{{n\left( {\Sigma \quad {XY}} \right)} - {\left( {\Sigma \quad X} \right)\left( {\Sigma \quad Y} \right)}}{\sqrt{\left\lbrack {{n\quad \Sigma \quad X^{2}} - \left( {\Sigma \quad X} \right)^{2}} \right\rbrack \left\lbrack {{n\quad \Sigma \quad Y^{2}} - \left( {\Sigma \quad Y} \right)^{2}} \right\rbrack}}} & (2)\end{matrix}$

[0050] where:

[0051] R the Pearson Product Moment Correlation Coefficient;

[0052] n=the number of data samples acquired during the test period;

[0053] X=temperature readings obtained from the sensors 110; and,

[0054] Y=machine “drift” readings obtained from device 120.

[0055] As stated above, the values for Y correspond to the readingsobtained from the linear measurement device 120 at the end of each10-minute interval between data acquisition events. A series of “R²”correlation coefficient values are thereby calculated, one such “R²”value being calculated for each sensor 110, to provide a statisticalmeasurement of the degree to which temperature changes detected by thatsensor 110 directly correlates to changes in the length ΔL of the rail42, as detected by the linear measurement device 120. By definition, thecloser an “R²” value is to a coefficient reference of 1.0, the more thetwo variables analyzed thereby directly correlate with one another.Accordingly, the “R²” values are compared for all sensors 110, and thesensor 110 having an “R²” value closest to 1.0 is determined to be thesensor 110 most representative of the location of the “effective”temperature of the machine 10. Temperature measurements of the machine10, then, for example, to perform thermal expansion/contractionmeasurements, should be taken from the sensor 110 having an “valueclosest to 1.0. Where none of the “R²” values of the sensors 110 areclose to 1.0, such as, for example, all sensor “R²” values being lessthan 0.5, it should be determined that none of the sensors 110 arelocated in a position on the machine 10 which sufficiently representsthe “effective” temperature of the machine 10, and the sensors 110should be repositioned and the test procedure repeated until an “R²”value sufficiently close to 1.0 is obtained.

[0056] To determine the “effective” thermal coefficient α of the machine10, and more particularly for the purpose of illustration, of the secondrail 42 of the machine 10, along axis “X₂”, the temperature dataacquired from the sensor 110 having an “R²” value closest to 1.0 isplotted against the “drift” measurements acquired from the linearmeasurement device 120. With reference to FIG. 3, a linear plot isprepared of temperature changes ΔT vs. thermal “drift” ΔL and aleast-squares line is fit over the plot thereof. According to Equation(1), above, the slope of the least squares line on a plot of ΔT vs. ΔLis the rate of change of ΔL with respect to ΔT. The “effective” thermalcoefficient α of the machine, with respect to the “X²” axis, is theslope of the least squares fit line of FIG. 3 divided by the initiallength L of the machine member, which in the present invention is thetest length L_(T).

[0057] Because the thermal coefficient α is derived empirically usingthe above test procedure, it is referred-to herein as an “effective”thermal coefficient α, to distinguish it from the “textbook” valuethereof. In many cases, the “effective” thermal coefficient α willdiffer from the “textbook” value thereof and differences therebetween,say on the order of less than 50% will typically be acceptable. However,where the determined “effective” thermal coefficient α differs greatlyfrom the textbook” value thereof, say on the order of greater than ±50%,the test analyst must use engineering judgment to determine whether thetest should be repeated, and if so, whether the sensors 110 should berepositioned.

[0058] Obtaining the effective coefficient of expansion and using thatparameter for calibrating the machine initially provides the basis forfuture rechecks of the machine's calibration for correctness. By notusing the correct coefficient initially means that when the machine isrechecked, if the temperature factors are different at the machine, thenew calibration values will never match the initial setup and cause aresetting of the values. The effort for resetting is time consuming andcauses loss of available production time. Even if the NC program wereadjusted to allow production of a good part with an initially incorrectset of machine compensation values, the recheck of the machine willcause a resetting of compensation values and cause the machine toproduct a different part. Purpose of rechecking the machine is formaintaining proper values even if the machine were to drift or changeover time. One would never know if changes had occurred to the machineduring maintenance check if an incorrect coefficient of expansion wereused. If parts started showing errors, one would never know if theerrors were due to process changes or machine changes. By using a methodthat obtains the effective coefficient of expansion initially for themachine installation means that a proper baseline for machinecalibration is established and can be used again and again duringmaintenance checks.

[0059] With reference to FIG. 4, the value of the “effective” thermalcoefficient α relative to an axis of movement may be used in calibratingmovement of machine components along such axis to compensate for thermalexpansion thereof A typical compensation table 200 is in the form of alook-up table residing in (or otherwise accessible to) the machinecontrol system and includes a first column 202 of commanded positionvalues 203 representing positions, locations or displacements which theNC program may command a machine member, for example, the head 60 of themachine tool 10 shown in FIG. 2, to move along an axis, for example, the“X” axis shown in FIG. 2. The compensation table 200 further includes asecond column 204 of mechanical offset values 205, one such mechanicaloffset value 205 corresponding to one of each of the commanded positionvalues 203 of the first column 202. The mechanical offset values 205represent some offset value used to compensate for mechanicalpositioning errors of the machine 10, for example, due to slack in thedrive mechanisms thereof and can be determined by any conventionalmechanical calibration procedure.

[0060] The compensation table 200 also includes a third column 206 ofmachine thermal offset values 207, one such machine thermal offset value207 corresponding to one of each of the commanded position values 203 ofthe first column 202. The third column 206 represents values calculatedusing Equation (1) to compensate for thermal positioning errors of themachine due to thermal expansion thereof. For the purpose of usingEquation (1) to calculate such machine thermal offset values 207 (whichare represented in Equation (1) by the term ΔL) the “effective” thermalcoefficient α of the machine 10 (which is determined according to theprocedure described hereinabove) may be used. The term ΔT represents thedifference between the operating temperature (which is represented inEquation (1) by the term T_(f)) of the machine 10 and a referencetemperature (T_(i)) of 68° F. (20° C.).

[0061] Because the values 207 of the third column 206 depend directly onthe operating temperature, changes in operating temperature will causechanges in the values 207. However, even though the operatingtemperature may vary during machining operations, such variancetypically results in only modest changes to the values 207 of the thirdcolumn 206. As such, it is preferable to provide a static compensationtable 200 for a predetermined operating temperature range T₁-T₂, forexample, between T₁=60° F. (15.56° C.) and T₂=70° F. (21.11° C.),wherein the values 207 of the third column 206 are calculated based onan average temperature within the temperature range T₁-T₂. A secondcompensation table 300 may be provided for a second temperature rangeT₃-T₄, wherein the second compensation table 300 includes first andsecond columns 302, 304, respectively, containing values which areidentical to columns 202, 204, respectively, of compensation table 200,as well as a third column 306 of machine thermal compensation values 307calculated using Equation (1) based upon an average temperature of thesecond temperature range T₃-T₄. Additional compensation tables, such asthird and fourth compensation tables 400, 500, respectively, maylikewise be provided for additional temperature ranges T₅-T₆ and T₇-T₈,respectively.

[0062] At the start of a machining operation, the operating temperatureof the machine must be entered into the machine control such that themachine control may select the proper compensation table 200, 300, 400,500 to be used. According to a preferred embodiment hereof, a machineoperator manually inputs the operating temperature of the machine 10into the machine control, which compares the operating temperature withthe available temperature ranges T₁-T₂, T₃-T₄, T₅-T₆, T₇-T₈ and selectsthe proper compensation table 200, 300, 400, 500 based thereon. Motionof the machine, then, is “compensated” for both mechanical and thermalpositioning errors by adding corresponding values 205, 207 from thesecond and third columns 204, 206, respectively, to the correspondingcommanded position value 203 from the first column 202. In this manner,modification of the NC program is not required in order to compensatefor thermal expansion/contraction of the machine 10 because the machine10 has been calibrated to compensate for such thermal characteristics.

[0063] The operating temperature of the machine 10 may be entered intothe machine control by alternative means. For example, the machinecontrol may acquire a temperature reading from a thermocouple locatedsomewhere on the machine. As described above, the “effective”temperature of the machine 10 corresponds to the sensor 110 (FIG. 2)where the temperature readings obtained thereby during the thermalcalibration procedure according to the present invention result in an“R²” value closest to 1.0. Rather than requiring a machine operator tomanually input the operating temperature of the machine 10 into themachine control, the operator may instruct the machine control toacquire an operating temperature reading from the sensor 110 at thelocation of the “effective” temperature of the machine 10.Alternatively, the machine control may automatically acquire theoperating temperature at the some time either before or during themachining operation. For example, the NC program may include aninstruction for the machine control to acquire automatically theoperating temperature as the NC program is loaded into the machinecontrol or executed. Once the operating temperature is obtained by themachine control, the machine control will select the proper compensationtable 200, 300, 400, 500 as described above.

[0064] According to an alternative embodiment of the present invention,the compensation table 200 does not include a third column 206. Rather,thermal offset values are calculated dynamically as the machine controlreceives instructions from the NC program That is, first and secondcolumns 202, 204, respectively, are populated with values 203, 205,respectively, as described above. However, thermal offset values arecalculated as position commands are received by the machine control.According to the method of the present embodiment, each time the machinecontrol receives a commanded position instruction from the NC program,the machine control obtains a value for the mechanical offsetcorresponding to the position instruction, acquires an “effective”machine temperature reading and calculates a thermal offset value usingEquation (1). The offset values are then added to the commanded positionvalue as descried above to compensate for both mechanical and thermalpositioning errors.

[0065] According to another aspect of the present invention, the methodhereof may be used to calibrate the machine tool 10 for positioningerrors due to machining a workpiece having a coefficient of thermalexpansion which is different than the “effective” thermal coefficient αof the machine 10. With reference to FIG. 5, the compensation table 200includes a fourth column 208 of workpiece thermal offset values 209, onesuch workpiece thermal offset value 209 corresponding to one of each ofthe commanded position values 203 of the first column 202. The fourthcolumn 208 represents values calculated using Equation (1) to compensatefor thermal positioning errors of the machine 10 due to thermalexpansion of the workpiece “W” relative to the machine 10. For thepurpose of using Equation (1) to calculate such workpiece thermal offsetvalues 209 (which are represented in Equation (1) by the term ΔL), anyaccepted value for the coefficient of thermal expansion of the materialused to construct the workpiece may be used, or an “effective” thermalcoefficient thereof may be calculated. The term ΔT represents thedifference between the workpiece operating temperature (which isrepresented in Equation (1) by the term T_(f)) and a referencetemperature of 68° F. (20° C.).

[0066] The compensation table 200 may be modified to permit selection ofvarious workpiece materials. Fifth and sixth columns 210, 212,respectively, may be provided, each representing material thermal offsetvalues 211, 213 calculated using Equation (1) based on unique workpiecematerials. For example, the fourth column 208 may represent workpiecethermal offset values 209 calculated with Equation (1) based upon thecoefficient of thermal expansion of aluminum, the fifth column 210 mayrepresent workpiece thermal offset values 211 calculated with Equation(1) based upon the coefficient of thermal expansion of titanium and thesixth column 212 may represent workpiece thermal offset values 213calculated with Equation (1) based upon the coefficient of thermalexpansion of steel. Of course, more or less than the number of columnsdescribed herein may be provided without departing from either thespirit or the scope of the present invention.

[0067] Prior to the machining operation, the machine operator may entermanually into the machine control the material used to construct theworkpiece to be machined. Based upon the operator's input, the machinecontrol will access either the fourth, fifth or sixth column 208, 210,212, respectively, and read the workpiece thermal offset values 209,211, 213, respectively, thereof, together with the mechanical offsetvalues 205 of the second column 204 and the machine thermal offsetvalues 207 of the third column 206, to calculate a total offset value tocompensate for all mechanical, machine thermal and workpiece thermalpositioning errors. Alternatively, the NC program may include aninstruction to the machine control concerning which column, as betweencolumns 208, 210, 212, for reading workpiece thermal offset values.

[0068] As with the method described above with reference to FIG. 4,calculation of the workpiece thermal offset values 209, 211, 213 usingEquation (1) requires the temperature of the workpiece to be known orapproximated. The workpiece temperature may be manually entered into themachine control by the machine operator or it may be acquiredautomatically by the machine control, which may read data from atemperature sensor positioned on or near the workpiece at any suitablelocation therefor. As described above, where the machine controlacquires the workpiece temperature reading automatically, such may be inresponse to an instruction by the operator or in response to aninstruction provided in the NC program Additional compensation tables300, 400, 500 may be provided for temperature ranges T₃-T₄, TS-T₆ andT₇-T₈, respectively, where compensation table 200 is provided fortemperature range T-T₂ as described above. However, each compensationtable 300, 400, 500 may include fourth, fifth and sixth columnsrepresenting thermal offset values for specific material selections,such as aluminum, titanium and steel, wherein the compensation table isselected in response to temperature input and the respective workpiecethermal offset column thereof is selected in response to workpiecematerial selection. In this manner, the machine tool 10 may becalibrated to compensate for mechanical, machine thermal and workpiecethermal positioning errors without modifying the NC program.

[0069] Where a member being tested according to the method hereof is notconstrained whatsoever, the method hereof may be used to determine the“effective” thermal coefficient of the member. Accordingly, the presentinvention provides a method for determining the “effective” value of thethermal coefficient of a machine member. Moreover, the present inventionprovides a method for determining the “effective” value of the thermalcoefficient of a machine member, with reference to the environmentalconditions surrounding it.

[0070] As described above, the present invention provides a method fordetermining an “effective” value of the thermal coefficient of a machinecomprised of members constructed of materials having differingindividual thermal coefficient values. Moreover, the present inventionprovides a method for determining the “effective” value of the thermalcoefficient of a machine comprised of members which are constrained fromfreely moving in response to changes in the temperatures thereof.

[0071] Furthermore, as described above, the present invention provides amethod for determining an “effective” temperature of a machine, whichsuch “effective temperature” thereof may be used, for example, inperforming thermal expansion calculations.

[0072] Moreover, as described above, the present invention provides amethod for calibrating a machine wherein the true thermalcharacteristics of the machine are closely approximated, such as, withreference to an “effective” value of the thermal coefficient thereof.The present invention furthermore provides a method for calibrating amachine wherein the thermal characteristics of a workpiece to bemachined thereby are incorporated therein, and also provides a methodfor calibrating a machine wherein the thermal characteristics of aworkpiece to me machined thereby are incorporated thereinto, and whereina plurality of workpiece materials may be considered.

[0073] While the invention has been illustrated with reference to one ormore preferred embodiments hereof, and such preferred embodiments havebeen described in considerable detail with reference to the drawings, itis not the intention of applicants that the invention be restricted tosuch detail. Rather, it is the intention of the applicants that theinvention be defined by all equivalents of the preferred embodimentsfalling within the scope hereof.

We claim:
 1. A method for calibrating a machine to compensate forthermal expansion/contraction thereof, characterized in that said methodcomprises the steps of determining an effective thermal coefficient ofsaid machine; and, generating a machine thermal compensation value forat least one of a predetermined number of preselected position values,said machine thermal compensation value being based on said effectivethermal coefficient of said machine.
 2. The method of claim 1, furthercharacterized in that said step of determining an effective thermalcoefficient of said machine further comprises the steps of (a) selectingat least one predetermined location on said machine to monitor during atest period; (b) monitoring a distance between a first portion of saidmachine and a second portion of said machine; (c) acquiring atemperature reading at said at least one predetermined location; (d)recording said distance and said temperature reading when saidtemperature reading is acquired and associating said distance with saidtemperature reading; (e) repeating said steps (b)-(d) until said testperiod has expired; (f) determining whether a sufficiently linearrelationship exists between said distances and said temperature readingsrecorded in step (d); (g) repeating said steps (a)-(f) until saidsufficiently linear relationship exists; and, (h) selecting saideffective thermal coefficient based upon said linear relationship. 3.The method of claim 2, further characterized in that said step ofdetermining whether a sufficiently linear relationship exists comprisesthe step of performing a statistical analysis on said recorded distancesand said recorded temperature readings.
 4. The method of claim 3,further characterized in that said step of performing a statisticalanalysis comprises the steps of determining a correlation coefficient;and, comparing said correlation coefficient with a coefficientreference.
 5. The method of claim 4, further characterized in that saidstep of determining a correlation coefficient comprises the step ofdetermining a Pearson Product Moment Correlation Coefficient.
 6. Themethod of claim 2, further characterized in that said at least onepredetermined location includes one predetermined location.
 7. Themethod of claim 2, further characterized in that said distances arecollinear.
 8. The method of claim 2, further characterized in that saidtemperature readings are acquired at a predetermined frequency.
 9. Themethod of claim 8, further characterized in that said predeterminedfrequency has a period of 10 minutes.
 10. The method of claim 2, furthercharacterized in that said test period is at least 24 hours.
 11. Themethod of claim 2, further characterized in that said first portion ofsaid machine has a first thermal coefficient, said second portion ofsaid machine has a second thermal coefficient and said first thermalcoefficient is different from said second thermal coefficient.
 12. Themethod of claim 2, further characterized in that said first portion ofsaid machine is moveable relative to said second portion of saidmachine.
 13. The method of claim 12, further characterized in that saidfirst portion of said machine is constrained from moving freely relativeto said second portion of said machine.
 14. The method of claim 1,further characterized in that said machine thermal compensation value isbased on an effective temperature of said machine.
 15. The method ofclaim 14, further characterized in that said effective temperature ofsaid machine is acquired in response to an instruction from an NCprogram.
 16. The method of claim 1, further characterized in that saidmethod further comprises the steps of: selecting a thermal coefficientof a workpiece to be machined by the machine; generating a workpiecethermal compensation value based upon said thermal coefficient of saidworkpiece; and, adding said workpiece thermal compensation value to saidmachine thermal compensation value to obtain a total thermal offsetcompensation value.
 17. The method of claim 16, further characterized inthat said step of selecting a thermal coefficient of a workpieceincludes the step of selecting a material to be machined, said materialhaving said thermal coefficient associated therewith.
 18. The method ofclaim 16, further characterized in that said thermal coefficient of saidworkpiece is selected in response to an instruction from an NC program.